Cyclotomic p-adic multi-zeta values

2017/01/20 by Unver, Sinan
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1701.05729

Abstract

The cyclotomic p-adic multi-zeta values are the p-adic periods of π₁(\mathbbG_m ∖ μ_M,⋅), the unipotent fundamental group of the multiplicative group minus the M-th roots of unity. In this paper, we compute the cyclotomic p-adic multi-zeta values at all depths. This paper generalizes the results in [6] and [7]. Since the main result gives explicit formulas we expect it to be useful in proving non-vanishing and transcendence results for these p-adic periods and also, through the use of p-adic Hodge theory, in proving non-triviality results for the corresponding p-adic Galois representations.

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